2020/08/26 by Yang Han, Han, Yang
Computer Science · Mathematics · #16E30 #16E40 #16E45 #16G10 #18G35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Matrix Theory and Algorithms #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.KT #math.RA #math.RT #msc:16E30 #msc:16E40 #msc:16E45 #msc:16G10 #msc:18G35
paper · pdf · doi:10.48550/arxiv.2008.11457
33 pages; a few typos are corrected
openalex publication_date 2020/08/26 · arxiv created 2020/09/07 · arxiv updated 2020/09/08 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The Hirzebuch-Riemann-Roch (HRR) and Lefschetz type formulas for finite dimensional elementary algebras of finite global dimension are explicitly given. They have cohomological, homological, Hochschild cohomological and Hochschild homological four versions, and module, bimodule, module complex and bimodule complex four levels. For this, the dimension matrix of a bimodule (complex) and the trace matrix of a bimodule (complex) endomorphism are introduced. It is shown that Shklyarov pairing, Chern character and Hattori-Stallings trace can be concretely expressed by Cartan matrix, dimension vector and trace vector in this situation. Furthermore, the HRR and Lefschetz type formulas for finite dimensional elementary algebras of finite global dimension and dg algebras are compared.